State of charge estimation of ultracapacitor based on forgetting factor recursive least square and extended Kalman filter algorithm at full temperature range

Abstract

State of charge (SOC) of ultracapacitor plays an important role in the energy management optimization of hybrid energy storage system for electric vehicles. In addition to the perfection of the model and the SOC estimation algorithm, the parameter identification method and temperature factor should also be considered. In this paper, an ultracapacitor test platform is established, the characteristic parameters of ultracapacitor at full temperature range are obtained. This paper uses the forgetting factor recursive least squares algorithm (FFRLS) to identify the parameters of the second-order equivalent circuit model of ultracapacitor online. The extended Kalman filter (EKF) algorithm is used to estimate the SOC of ultracapacitor cell. The results show that: (1) FFRLS algorithm can identify $R_0$ , $R_1$ , $R_2$ , $C_1$ , and $C_2$ values of ultracapacitor at full temperature range. Under the hybrid pulse power characterization working condition, the average mean absolute error between the estimated voltage and the actual voltage is about 0.0132 V. (2) EKF algorithm has a good adaptability to estimate SOC of ultracapacitor under different temperatures and working conditions. The SOC estimation error under different working conditions is low. From the perspective of mean square error, the estimation error at -20 °C is the lowest. (3) FFRLS and EKF joint estimation algorithm with good robustness and reliability can be used to estimate the SOC of ultracapacitor under different temperatures and working conditions. This study can provide a useful guidance for the parameter identification and SOC estimation of ultracapacitor for electric vehicle at different temperatures.

Keywords: Extended Kalman filter; Forgetting factor recursive least squares; Parameter identification; State of charge; Ultracapacitor.